Remark 2.2 
It follows from [1]} that \(\overline{\mathcal {J}}_{g,n}\)  is isomorphic to the algebraic stack parametrizing pairs \((\mathcal {X}\rightarrow S, \mathcal {I})\)  consisting of a family \(\mathcal {X}\rightarrow S\)  of \(n\) -marked genus \(g\)  stable curves and a coherent sheaf \(\mathcal {I}\)  on \(\mathcal {X}\) , flat over \(S\) , whose geometric fibers are rank-1 torsion-free sheaves.
In this alternative description:
